Ok, here are my tips & tricks to get through (almost) the whole game without using your weapon (only ninpo and projectiles).
First I did a normal game (on Acolyte) with the DS and just gathered everything but used nothing! Keep all the LotG and 1000Gods and all the Jewels (exept the Demon seal) in your inventory.
So I started the run with about 220.000 essence all weapons maxed out, 7 (or 8) Lives of a 1000 Gods, 18 Life of the Gods and 2 Spirit of the devils (and you can buy 2 more in this run) and all health items at max.
First and best tip;
don't fight if you don't have to!! This is not a Karma-run (this is the chicken-run) and you don't need any items anymore, so run passed all fights, boxes, savepoints and shops if you can. It's amazing how much you can actually skip. When you do have to fight the IS are your best friends so don't be stingy with them and always max them out when you're at a shop. If you run out of IS, use the Wind-shuriken; a fully charged one can kill ninja's with 1 hit.
Getting through the Chapters isn't all that hard but the Bosses can be. The hardest are Alexei, Genshin and Zedonius (ok and Elizebet). Genshin can only be killed with IS and they have to be timed right as well! They only hit when he is attacking!
Alexei cost me a Spirit of the Devils (every time) and a Talisman and 3 mushrooms; you need the Void-ninpo for him (projectiles don't work on him) but he has this spinning electric move he does when you use ninpo making him invulnerable for ninpo so you need some luck. (oh and when you fight him in Ch.13 be carefull; if you, by accident, hit the caged chick with your ninpo instead of Alexei your game is over!). For the last part of his healthbar (in Ch.13) you need to switch to your Flame Phoenix ninpo cuz he the void-ninpo won't hit him anymore.
Save your Spirit of the Devils and Talisman for those Boss-fights! Don't forget that when you are at a shop you have to buy all the items you missed in order to get the other 2 Spirit of the Devils (If Muramasu does not have a place available in his shop you won't get them). Don't worry you'll gather enough essence with the kills you make to be able to buy everything (I ended up with 120.000 to spare at the last savepoint)
Another good tip is; know where the red-essence boxes are and use them to your advantage; it makes your life a lot easier when you can ninpo-spam your way past certain tough points knowing you can refill your ninpo. You can use this guide if you have to:
http://www.wikicheats.com/index.php/Ninja_Gaiden_2_-_XB360/Walkthrough(don't forget the arrow targets in Ch.11 (the big fight!) give red/blue and yellow essence when you shoot them).
I made it all the way to Ch.14 to the save-point just before the bloodpool with the eels prior to fighting Genshin (for the last time) and Elizebet. It is probably possible to get through this fight without using weapons but it wasn't worth the hassle for me. Genshin is almost impossible to hit with IS this time and then you get Elizebet right after, so my weaponless run ended here. Left me with just 1 chapter to walk through with all the different weapons to finally get 1000 points.
Have fun!
Once I jumped in the air and missed, I landed on the floor and fell off..